Problem: Kevin is 2 times as old as Brandon. 21 years ago, Kevin was 9 times as old as Brandon. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and Brandon. Let Kevin's current age be $k$ and Brandon's current age be $b$ The information in the first sentence can be expressed in the following equation: $k = 2b$ 21 years ago, Kevin was $k - 21$ years old, and Brandon was $b - 21$ years old. The information in the second sentence can be expressed in the following equation: $k - 21 = 9(b - 21)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $b$ and substitute it into our second equation. Solving our first equation for $b$ , we get: $b = k / 2$ . Substituting this into our second equation, we get: $k - 21 = 9($ $(k / 2)$ $- 21)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 21 = \dfrac{9}{2} k - 189$ Solving for $k$ , we get: $\dfrac{7}{2} k = 168$ $k = \dfrac{2}{7} \cdot 168 = 48$.